Question

At NTP, $5.6$ litre of a gas weighs $8$ gram. The vapor density of gas is found to be.
A. $32$
B. $40$
C. $16$
D. $8$

Answer 1

Hint: We know that NTP is Normal Temperature and Pressure which is defined as a temperature of ${20^0}C$ and $1$ atmosphere. Vapor density is defined as the density of a vapor in relation to that of hydrogen. Vapor density can tell us whether a gas is denser or less dense than air.

Complete step by step answer:
To find the vapor density first we have to calculate the number of moles.
Since we know that, $1$ mole of gas occupies $22.4L$ at normal temperature and pressure.
Number of moles can be given by the equation.
$Number{\text{ }}of{\text{ }}moles = \dfrac{{Given{\text{ }}volume}}{{22.4}}$
Therefore, by substituting the values from the question we get,
$ = \dfrac{{5.6}}{{22.4}}$
$ = 0.25moles$ $(equation1)$
Number of moles can also be given by the equation.
$Number{\text{ }}of{\text{ }}moles = \dfrac{{Given{\text{ }}mass}}{{Molecular{\text{ }}mass}}$
Therefore, by substituting the values from the question and $0.25$ from $equation1$ we get,
\[0.25 = \dfrac{8}{{Molecular{\text{ }}mass}}\]
$Molecular{\text{ }}mass = \dfrac{8}{{0.25}}$
$ = 32g$ $(equation2)$
To find the vapor density we use the formula,
$Vapour{\text{ }}density = \dfrac{{Molecular{\text{ }}mass}}{2}$
By substituting the value of molecular mass from $equation2$
$ = \dfrac{{32}}{2}$
$ = 16$

So, the correct answer is Option C.

Additional information:
Vapor density is the relative weight of a gas compared to that of air. It is a unitless quantity. If the vapor density is greater than one the gas usually sinks in air and it the value of vapor density is less than one gas usually rises in the air
Molecular mass: It can be defined as the sum of atomic masses of all the atoms in the molecule.
Molar mass: It is the mass of one mole of one whole compound.

Note: Similar to NTP there is STP which is Standard Temperature and Pressure. So according to STP the standard temperature was fixed as $273.15K$and an absolute pressure of ${10^5}Pa$.
Atoms can be defined as the smallest part of an element.
Atomic mass can be defined as the mass of one single atom which is measured in one atomic mass unit.
One a.m.u equals one-twelfth the mass of one isotope of carbon atom.
$1a.m.u = \dfrac{1}{{12}}mass{\text{ }}of{\text{ }}{C^{12}}{\text{ }}atom$